Abstract
In this paper, we develop a new method for finding an optimal bidding strategy in sequential auctions, using a dynamic programming technique. The existing method assumes the utility of a user is represented in an additive form. Thus, the remaining endowment of money must be explicitly represented in each state. On the other hand, our method assumes the utility of a user can be represented in a quasi-linear form, and representing the payment as a state-transition cost. Accordingly, we can obtain more than an $m$-fold speed-up in the computation time, where $m$ is the initial endowment of money. Furthermore, we have developed a method for obtaining a semi-optimal bidding strategy under budget constraints.
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